Evaluating the Training Performance of Artificial Neural Network Using Small Time Series Segments of The Lorenz Chaotic System

2018 ◽  
Author(s):  
Lei Zhang
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Artificial Neural Network ◽  
Chaotic System ◽  
Small Time ◽  
Training Performance ◽  
Lorenz Chaotic System ◽  
Artificial Neural

Chaotic System Design Based on Recurrent Artificial Neural Network for the Simulation of EEG Time Series

2019 ◽  
Vol 13 (1) ◽  
pp. 25-35
Author(s):  
Lei Zhang
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Artificial Neural Network ◽  
Chaotic System ◽  
Research Work ◽  
Euler Method ◽  
Open Loop ◽  
Training Data ◽  
Artificial Neural ◽  
Artificial Neural Network Ann

Electroencephalogram (EEG) signals captured from brain activities demonstrate chaotic features, and can be simulated by nonlinear dynamic time series outputs of chaotic systems. This article presents the research work of chaotic system generator design based on artificial neural network (ANN), for studying the chaotic features of human brain dynamics. The ANN training performances of Nonlinear Auto-Regressive (NAR) model are evaluated for the generation and prediction of chaotic system time series outputs, based on varying the ANN architecture and the precision of the generated training data. The NAR model is trained in open loop form with 1,000 training samples generated using Lorenz system equations and the forward Euler method. The close loop NAR model is used for the generation and prediction of Lorenz chaotic time series outputs. The training results show that better training performance can be achieved by increasing the number of feedback delays and the number of hidden neurons, at the cost of increasing the computational load.

Chaotic System Design Based on Recurrent Artificial Neural Network for the Simulation of EEG Time Series

2022 ◽  
pp. 1510-1521
Author(s):  
Lei Zhang
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Artificial Neural Network ◽  
Chaotic System ◽  
Research Work ◽  
Euler Method ◽  
Open Loop ◽  
Artificial Neural ◽  
Artificial Neural Network Ann ◽  
Dynamic Time

Electroencephalogram (EEG) signals captured from brain activities demonstrate chaotic features, and can be simulated by nonlinear dynamic time series outputs of chaotic systems. This article presents the research work of chaotic system generator design based on artificial neural network (ANN), for studying the chaotic features of human brain dynamics. The ANN training performances of Nonlinear Auto-Regressive (NAR) model are evaluated for the generation and prediction of chaotic system time series outputs, based on varying the ANN architecture and the precision of the generated training data. The NAR model is trained in open loop form with 1,000 training samples generated using Lorenz system equations and the forward Euler method. The close loop NAR model is used for the generation and prediction of Lorenz chaotic time series outputs. The training results show that better training performance can be achieved by increasing the number of feedback delays and the number of hidden neurons, at the cost of increasing the computational load.

A Novel Intuitionistic Fuzzy Time Series Method Based on Bootstrapped Combined Pi-Sigma Artificial Neural Network

2021 ◽  
Vol 01 ◽  
Author(s):  
Eren Bas ◽  
Erol Egrioglu ◽  
Emine Kölemen
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Artificial Neural Network ◽  
Stock Exchange ◽  
Fuzzy Time Series ◽  
Time Series Models ◽  
Intuitionistic Fuzzy ◽  
Forecasting Methods ◽  
Time Series Method ◽  
Artificial Neural

Background: Intuitionistic fuzzy time series forecasting methods have been started to solve the forecasting problems in the literature. Intuitionistic fuzzy time series methods use both membership and non-membership values as auxiliary variables in their models. Because intuitionistic fuzzy sets take into consideration the hesitation margin and so the intuitionistic fuzzy time series models use more information than fuzzy time series models. The background of this study is about intuitionistic fuzzy time series forecasting methods. Objective: The study aims to propose a novel intuitionistic fuzzy time series method. It is expected that the proposed method will produce better forecasts than some selected benchmarks. Method: The proposed method uses bootstrapped combined Pi-Sigma artificial neural network and intuitionistic fuzzy c-means. The combined Pi-Sigma artificial neural network is proposed to model the intuitionistic fuzzy relations. Results and Conclusion: The proposed method is applied to different sets of SP&500 stock exchange time series. The proposed method can provide more accurate forecasts than established benchmarks for the SP&500 stock exchange time series. The most important contribution of the proposed method is that it creates statistical inference: probabilistic forecasting, confidence intervals and the empirical distribution of the forecasts. Moreover, the proposed method is better than the selected benchmarks for the SP&500 data set.

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